Reduce the coordination problem
Hand independence is easier to study when each hand has a clearly defined job. Hold a left-hand bass note for four beats while the right hand plays a light chord on beats one and three. Count aloud and let the left hand remain still between its attacks. If it retriggers when the right hand plays, slow down and rehearse only the moment where the hands differ. Do not begin with an elaborate bass pattern and a busy right hand, because too many moving parts make the source of the error hard to identify.
Practice the combined rhythm away from pitches
Tap the left-hand events on one leg and the right-hand events on the other. Speak the count while noticing which attacks happen together and which happen alone. This removes note finding from the task. Return to one chord on the keyboard and repeat the same coordination. Use a relaxed touch and take short breaks so the exercise does not become a rigid muscular pattern. Accuracy at a manageable tempo matters more than forcing the hands through a faster version that changes every repetition.
Introduce one harmonic change
Alternate two familiar chords, changing both hands at the start of each measure while preserving their different rhythms inside the measure. Choose comfortable voicings so that large jumps do not add another challenge. Once the pattern feels stable, use it on a short verified progression from AudioChords. If the coordination fails at one transition, practice that boundary rather than restarting the song. End by adding a hummed melody or listening to the track. The purpose of the exercise is an accompaniment you can maintain while attending to music, not an isolated trick that consumes all your concentration.